a) In a group of 60 students, 15 liked maths only, 20 liked science only and 5 did not like
any of two subjects?
(i) How many of them liked at least one subject?
(ii) Find the number of students who liked both the subjects.
(iii) How many of them liked maths?
(iv) How many of them liked science?
(v) Represent the result in a Venn diagram.
PLZ PLZ HELP.........
Answers
Part (i)
We have 60 students total, and 5 didn't like any of the two subjects, so that must mean 60-5 = 55 students liked at least one subject.
Answer: 55=========================================================
Part (ii)
We have 15 who like math only, 20 who like science only, and 55 who like either (or both). Let x be the number of people who like both classes.
We can then say
15+20+x = 55
x+35 = 55
x = 55-35
x = 20
This means 20 people liked both subjects
Answer: 20=========================================================
Part (iii)
There are 15 people who like math only, and 20 who like both. Therefore, there are 15+20 = 35 people who like math (and some of these people also like science)
Answer: 35=========================================================
Part (iv)
We'll follow the same idea as the previous part. There are 20 people who like science only and 20 who like both subjects. That yields 40 people total who like science (and some of these people also like math).
Answer: 40=========================================================
Part (v)
We'll draw a rectangle to represent the entire group of 60 students. This is considered the universal set. Inside the rectangle will be two overlapping circles to represent math (M) and science (S).
We'll have 15 go in circle M, but outside circle S to represent the 15 people who like math only. Then we have 20 go in circle S but outside circle M to show the 20 people who like science only. We have another copy of 20 go in the overlapped region between the circles. This is the 20 people who like both classes. And finally, we have 5 go outside both circles, but inside the rectangle. These are the 5 people who don't like either subject.
Note how all of the values in the diagram add up to 60
15+20+20+5 = 60
This helps confirm we have the correct values.
Answer: See the venn diagram below
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Answer:
124
Step-by-step explanation:
The diagonal of a rectangular field is 60 metres more than the shorter side. If the longer side is 30 metres more than the shorter side, find the sides of the field.
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Answer:
2)
3)
4)
5)
6)
Step-by-step explanation:
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Find the value of x in the triangle shown below.
Answers
Answer:
x ≈ 55.5°
Step-by-step explanation:
Using the Sine rule in the triangle
[tex]\frac{5}{sinx}[/tex] = [tex]\frac{5.7}{sin70}[/tex] ( cross- multiply )
5.7 sinx = 5 sin70° ( divide both sides by 5.7 )
sin x = [tex]\frac{5sin70}{5.7}[/tex] , then
x = [tex]sin^{-1}[/tex] ([tex]\frac{5sin70}{5.7}[/tex] ) ≈ 55.5° ( to the nearest tenth )
Answer:
[tex]x =55[/tex]°
Step-by-step explanation:
An isosceles triangle is a triangle with two congruent sides. One can see that the given triangle is an isosceles triangle, as two sides have a side length of (5) units. One property of an isosceles triangle is the base angles theorem. This theorem states that the angles opposite the congruent sides of an isosceles triangle are congruent. In this situation, this means that two angles have a measure of (x) degrees. As a given, the sum of angles in any triangle is (180) degrees. Thus, one can form an equation, and solve for the unknown, (x):
[tex]x + x + 70 = 180[/tex]
Simplify,
[tex]2x + 70 =180[/tex]
Inverse operations,
[tex]2x + 70 =180[/tex]
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Describe and correct the error in finding the volume of the pyramid.
Answers
Consider the triangle
Which statement is true about the lengths of the sides?
6 C5
45
O Each side has a different length.
O Two sides have the same length, which is less than
the length of the third side.
O The three sides have the same length
O The sum of the lengths of two sides is equal to the
length of the third side.
45
search
BI
59°F Clear
Answers
Answer:
b
Step-by-step explanation:
The triangle is an isoceles triangle since there are 2 equal angles. Hence, 2 sides would be the same length. Since its a right angled triangle, the hypotenuse (third side) would always be longer than the 2 equal sides.
Help plzzzz!!!!!!! thank you .
Answers
Answer:
120°
Step-by-step explanation:
<U + <T = 180
or, 6x-6+9x+21=180
or, 15x=165
or, x=11
so, <T = 9×11+21 = 120
Amber had 56 of a book of postage stamps. She used 26 of the book of postage stamps. Which fraction of the book of postage stamps does Amber have now?
Answers
An Step-by-step explanation: There are 56 stamps in total, and Amber used 26. So, she used 26/56. We need know which fraction has now. so she have 30/56 (becauase 56-26= 30). And by simplify, she have now 15/28 (if you simplify by 2)
41. If two fair coins are tossed what is the probability of getting at least one head? _____________
Answers
Answer:
3/4
Step-by-step explanation:
The possible outcomes when tossing two coins are
HH HT TH TT where H is heads and T is tails
There are 3 outcomes where we get at least one head
Positive outcomes over total outcomes
3/4
I NEEDDD HELPPP ITSSSSSS URGENTTTTT!!!
Answers
100 degrees
Step-by-step explanation:
measure of FHD = 65 + 35
measure of FHD = 100
Basically count/add up the total amount of degrees that are include in the angle <FHD.
-- (central angles)
So, 35 + 65 = 100 degrees
2. Use technology to graph, or graph by hand (on graph paper- MUST BE ACCURATE) each plan on the same set of axis (all three lines on the same graph – this is not a scatter plot! You must have connecting line segments). Assume that a maximum of attendees will be 50 (you will need to adjust the scale - wrench setting). Place a copy of your graph into this document. You must have labeled axis!!! To label your axis on Desmos, go to the wrench settings. (4 marks)
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Answer:
https://www.woboe.org/cms/lib8/NJ01912995/Centricity/Domain/905/Graphing-Packet%20Answers.pdf
Let me know if this helps!
Be a bit more specific on the question like what do you want us to do\
MORE INSTRUCTIONS THAN THE QUESTION
The polygons in each pair are similar. Find the missing side length.
Answers
Answer:
12
Step-by-step explanation:
We can say that two polygons are similar to each other if both of the polygons have the same shape and their corresponding sides are in the same proportion, hence the ratio of their corresponding sides are equal to each other.
As we can see from the problem since both of the polygons are similar, hence the ratio of their corresponding sides are in the same proportion, therefore let x represent the missing length, hence:
[tex]\frac{x}{15} =\frac{32}{40} =\frac{32}{40} \\\\\frac{x}{15} =\frac{32}{40} \\\\x=\frac{32*15}{40} \\\\x=12[/tex]
A 20 foot ladder rests against a wall. The ladder makes a 55° angle with the ground. How far from
the wall is the base of the ladder?
Answers
Answer:
11.5 foot (rounded to one decimal)
Step-by-step explanation:
x = 20×sin(35)
x ≈ 11.47153.. ≈ 11.5
Answered by GAUTHMATH
Graph the line that passes through (5, 5), and is perpendicular to a line whose slope is –2.
Answers
Answer:
y = 1/2x + 5/2
Step-by-step explanation:
y = 1/2x + b
5 = 1/2(5) + b
5 = 5/2 + b
5/2 = b
mark is making a square pen for his puppy. he wants the puppy to have 36 square feet of space to play in. he can use square roots to determine the length of one side of the square section so that he can be sure to purchase enough fencing for the pen. how is the side of the square pen related to the area ?
how long is one side of the square pen ?
how much fencing will mark need to purchase ?
someone please help me lol
Answers
Answer:
see below
Step-by-step explanation:
The area of a square is given by
A = s^2 where s is the side length
36 = s^2
Taking the square root of each side
sqrt(36) = sqrt(s^2)
6 = s
The side length of the pen is 6 ft
To find the perimeter of a square
P = 4s
P = 4*6 = 24
He will need 24 ft of fencing
What is an equation of the line that passes through the points (0, 8) and (-8, -4)?
Answers
Answer:
y = 1.2x + 2
Step-by-step explanation:
slope = (8 - 2)/(5 - 0) = 6/5y-intercept = (0, 2)y = (6/5)x + 2y = 1.2x + 2
Answer:
y=1.5x +8
Step-by-step explanation:
2+9 +11+98+99999999999999999
Answers
Answer:
1.000000000000012e+16
Step-by-step explanation:
uh
Horace is running a race. He wonders how fast he is running.
Which unit rates would be reasonable for Horace to use to describe how fast he is running?
Select each correct answer.
a miles per hour
b millimeters per minute
c kilometers per hour
d inches per hour
Answers
Answer:
C. Kiometers per hour. I think
Sam wants to write an equation to represent a proportional relationship with a constant of proportionality of 6 he write y = 6 + x
Answers
Answer:
y = 6x
Step-by-step explanation:
The equation representing a proportional relationship is
y = kx ← k is the constant pf proportionality
Here k = 6 , then
y = 6x ← equation of proportion
Answer:
She is not correct, she would need to have something before the y to know the answer
Step-by-step explanation:
hope this helps :)
This...ik what mean is I'm just trying to find what the original numbers would be?
Answers
Answer:
17.5
Step-by-step explanation:
all the 10 numbers added together equal 10*16 = 160
-this is because all of the numbers added, and then divided by 10 equals 16
so the numbers in total, added equal 160.
subtract 20 (7+13) from 160 = 140
divide by 8
140/8 = 17.5
17.5
Explanation 17×5 is five but 2×5 is seven so 7×10 is 10
plz give me this ans by explaining
Answers
Answer:
I don't know what to do so I just answered the volume of this tell me if I am wrong
Step-by-step explanation:
radius : 3.5 cm
volume : ?
now,
volume (v) : π × r (2)
: 22/7 × 3.5(2)
:22×3.5×3.5 by 7
therefore,
the volume is 38.5
WHERE ARE THE EXPERTS AND ACE!!!!!!! I NEED HELP PLS SHARE YO SMARTNESS!!!!! WILL GIVE BRAINLIEST AND RATE AND VOTE!!!
Answers
Answer:
D and C
Step-by-step explanation:
1) You can cross check using desmos.
2) cos(120) is - 0.5
Is the domain of an arithmetic sequence discrete or continuous? Is the range of an arithmetic sequence discrete or continuous?
Answers
Answer:
continuous, continuous
Step-by-step explanation:
The discrete domain are set of input variables that have numbers in an interval. A continuous domain has all numbers in an interval. The point representing the solution of an equation are distinct. The range of sequence is the merely a set of defines the sequence and is represented as X1, X2, X3, or N = 1, 2, 3.A pair of parallel lines is cut by a transversal: 15 degrees and 80 degrees are the lines What is the measure of angle x?
60 degrees
65 degrees
70 degrees
80 degrees
Answers
Step-by-step explanation:
=80°-15°=65°please mark this answer as brainlist
Determine which lines are parallel and which are not parallel. Explain your reasoning.
1. m∠3=69°, m∠7=71°
2. m∠3=76°, m∠8=114°
(please explain!!)
Answers
Answer:
If M and N are parallel, then the correspondent angles generated by the intersection with line R (or line S) should be equal.
So, if M and N are parallel, we should get that angles 2 and angle 4 are equal, as both of these are on the fourth quadrant of the intersection with the same line.
Similarly, if R and S are parallel, then correspondent angles generated by the intersection with line M (or line N) should be equal, this means that:
angle 3 and angle 7 should be equal.
Also remember that if we have two lines intersecting, generating 4 angles, any pair of two adjacent angles will always add to 180°.
Here we have two cases:
1) m∠3=69°, m∠7=71°
Here we can see that:
m∠3 ≠ m∠7
Thus, lines R and S are not parallel.
And here we do not have any information on the angles 1, 2, 5, and 6, so we can't compare the angles generated by line N with the ones generated by line M, so we can not know if lines N and M are parallel or not.
2) Now we have that:
m∠3=76° , m∠8=114°
Notice that angle 8 and angle 7 are adjacent, then we have that:
∠7 + ∠8 = 180°
And we know that:
∠8 = 114°
Then:
∠7 + 114° = 180°
∠7 = 180° - 114° = 76°
Then we have:
∠7 = ∠3
From this we can conclude that lines R and S are parallel.
(again, we can not do anything with lines N and M)
If a cylindrical vessel is 12 cm long and its surface area is 540 cm2, set up an
equation to find its radius.
Answers
Answer:
Option (1)
Step-by-step explanation:
Surface area of a cylindrical vessel is given by the expression,
Surface area = [tex]2\pi r^{2}+2\pi rh[/tex]
= [tex]2\pi r(r+h)[/tex]
Here, r = Radius of the vessel
h = Length of the vessel
By substituting the values of 'h' and surface area in the expression,
2πr(12 + h) = 540
Therefore, Option (1) will be the correct option.
Please help me it’s due in 2 mins
Answers
82.053°??
(Tried going as fast as I can)
Find the volume of a cone with radius 10 feet and height of 4 feet.
Answers
Answer:
[tex]\frac{400}{3} \pi[/tex]
Step-by-step explanation:
Formula for Cone: π[tex]r^{2}\frac{h}{3}[/tex]
Since we have all the components, we can find the volume of the cone.
R = 10
H = 4
π[tex]10^{2}\frac{4}{3}[/tex]
10×10 = 100
100π[tex]}\frac{4}{3}[/tex]
[tex]}\frac{4}{3}[/tex]×100
4 100 400
--- × ----- = ------
3 1 3
Answer: [tex]\frac{400}{3} \pi[/tex]
Hope this helped.
Find the volume of a cone with radius 10 feet and height of 4 feet.
Solution :Given Data :
Radius = 10 feet
Height = 4 feet
Formulae :
[tex] \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \star \: \blue{ \underline{ \overline{ \green{ \boxed{ \frak{{ \sf V}olume_{(Cone)} = \pi {r}^{2} \frac{h}{3}}}}}}}[/tex]
Putting the values we get
[tex] \frak{ Volume_{(Cone)} = 3.14 × (10)² × \frac{4}{3} }[/tex]
[tex] \frak{Volume_{(Cone)} = 3.14 × 100 × \frac{4}{3} }[/tex]
[tex] \frak{Volume_{(Cone)} = 314 \times \frac{4}{3} }[/tex]
[tex] \frak{Volume_{(Cone)} = 418.67 \: ft³ }[/tex]
Henceforth, the volume is 418.67 ft³
The corresponding edges of two similar containers are 56cm and 84cm.Find the ratio of the capacities
Answers
Answer:
8 : 27
Step-by-step explanation:
Given the ratio of sides of 2 similar objects = a : b , then
ratio of volumes = a³ : b³
Here ratio of sides = 56 : 84 = 2 : 3 , then
ratio of volumes = 2³ : 3³ = 8 : 27
